I take care of my 9 y/o sister because my mom is completely unable to take care of anyone. However, I do not possess her custody. I've asked my mom but she refuses to hand over anything from my sister, but I figired since I take care of her maybe I could, at least, claim her in the taxes which our mother refused to allow me to do. Is there a way to go about this situation?
The child's SSN cannot be used on two different tax returns. If your mother files first and claims the child, your tax return claiming her will be rejected. You can file it by mail and let the IRS sort out which of you could claim this child as a dependent. Be prepared to show proof that you provided over half the child's support-----you may need school records, proof of paying for medical care, anything you can gather up to prove that you cared for your sister.
That being said....we have no details from you.....so we do not know whether you can claim your sister.
IRS interview to help determine who can be claimed:
https://www.irs.gov/help/ita/who-can-i-claim-as-a-dependent
https://ttlc.intuit.com/questions/3113432-who-can-i-claim-as-my-dependent